2 Consider bivariate normal random vector (X, Y ) having joint probability density function: f(x, y) = 1 2XY p 1 2 exp ( 1 2(1 2) hx X X 2 2(x X)(y Y ) XY + y Y Y 2i ) , with < x < , < y < . Derive the conditional density of Y |X = x, i.e., simplify the expression f(y|X = x) = f(x, y) fX(x) , where f(x, y) is the joint density of X and Y and fX(x) is the marginal density of X. Note that fX(x) > 0 for all x